A321 pilot reported an ECAM F/CTL SLATS FAULT message on final. The flight crew performed a go-around and ran the QRH and checklists. The flight crew made another approach and landing at destination airport.

Narrative

ECAM F/CTL SLATS FAULT - Approach to Runway XXR at ZZZ. Broke off approach. Conducted ECAM and QRH; setting up for flaps 3; slats between 0 and 1; Vref plus 25 landing. Briefed; [priority handling requested]. Normal landing ZZZ XXL. On Day 0; ZZZZ-ZZZ; Aircraft X (A321 Neo). Captain (CA) is Pilot flying (PF); First Officer (FO) is PM. Normal departure; cruise and descent from ZZZZ to ZZZ. On approach to ILS XXR; PF called for flaps 1. At which point an ECAM F/CTRL SLATS FAULT was received. Slats indicated amber at position zero. Per ECAM; PM recycled flaps back to zero; then back to flaps 1. ECAM reappeared. PM notified Approach Control we needed to break off approach and work system fault. ZZZ Approach complied with giving delaying vectors at 3000 ft. assigned altitude. PF (CA) then transferred controls to the PM (FO) to begin the non-normal procedure. (PF now FO - PM now CA) CA also assigned radio duties to FO during the non-normal. PM (CA) completed the ECAM; then completed QRH using standard procedures. Noticed fuel was approximately 7.9; which led to a sense of urgency. QRH landing distance was determined to be 8;340 ft. According to previously determined landing numbers; ZZZ XXR available runway landing distance was 8486 ft. CA determined that was too close and determined Runway XXL (11;248 ft.) was more suitable. ILS XXL was loaded in the FMS with appropriate QRH directed speed changes. Although QRH directed landing distance was referenced and determined to be controlling; landing distances from ACARS were still obtained. Attempted to notify ZZZ base operations via VHF radio with no contact. (Possibility due to slant range distance to ZZZ?) Sent abbreviated ACARS message to Operations Control. Selected EMER CALL P/B for in-flight notification. Notified in-flight crew as to the situation; and briefed in-flight crew as to highlights. (Flight control slats stuck - what that meant to aircraft control on approach/landing. Estimated landing in 5 to 10 minutes. Expected normal landing. Fire trucks would be on the side of the runway). Then confirmed with each in-flight individually if they had any questions. Once in-flight complete; returned focus to landing. Side note - CA did not make the PA announcement nor did CA not request in-flight to make an announcement to the passengers. CA did not make the PA announcement as they overheard the #1 in-flight made a PA announcement and heard the word 'emergency' used. They did not hear the entire announcement.Aircraft control was passed back to the CA; (CA now PF - FO now PM). [Priority handling requested] with ATC; requested Crash Fire Rescue (CFR) to be standing-by at the side of the runway. Requested ILS XXL and ready to commence approach. Received ATC vectors to join ILS XXL outside of ZZZZZ at 2;000 feet; cleared ILS XXL approach. The PM pointed out the aircraft was in alternate law. Discussions as to when the aircraft was going to direct law. Determined to delay landing gear and deselection of auto-pilot until later than normal on the approach. CA reviewed out-loud with FO all tasks and what was the status of each task to ensure all obvious tasks were completed to the best of our ability. FO agreed all was complete. Once on approach; landing gear was lowered at approximately 1500 ft. AGL; landing checklist completed; 1;000 stable call completed. Auto-pilot was deselected at approximately 700 feet. Aircraft reverted to direct law. Normal landing and roll-out. Cleared the runway; stopped; and requested CFR to confirm tire/brake temperatures. CFR determined temperatures within limits. CA then made an announcement to passengers regarding the event; all is well and taxied to gate. After the landing checklist was completed with the exception of flaps were left at flaps 3. CFR followed/paced the aircraft all the way to the gate. CFR reevaluated brake temperatures once at the gate. Brake temperatures were within limits; CFR was cleared off with a thank you. Maintenance met aircraft atthe gate. Debrief with the entire crew was conducted once all passengers were off aircraft in jet way to due vomit smell in front of aircraft. During debrief with the crew; learned multiple passengers vomited during vectors at 3;000 feet due to turbulence.